Abstract
Problem posing (not only in lesson planning but also directly in teaching whenever needed) is one of the attributes of a teacher’s subject didactic competence. In this paper, problem posing in teacher education is understood as an educational and a diagnostic tool. The results of the study were gained in pre-service primary school teacher education. Students were asked to pose problems containing some given data (namely fractions). The subsequent analysis of the problems posed by the students revealed shortcomings in their conceptual understanding of fractions. Classroom-based joint reflection became the means of reeducation.
Similar content being viewed by others
Notes
Primary school teachers in the Czech Republic must complete 4–5 years of undergraduate courses designed especially for primary school teachers. Their undergraduate teacher education program includes courses in all subjects taught at the primary school level.
References
Baker, W., Czarnocha, B., Dias, O., Doyle, K. M., & Prabhu, V. (2009). On adult students learning fractions at a community college. Annales of Polish Mathematical Society, 5th Series, Didactica Mathematicae 32. Krakow, Poland. pp. 5–48
Behr, M., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91–125). New York: Academic.
Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale: LEA.
Charalambous, C. Y., & Pitta-Pantazzi, D. (2007). Drawing on theoretical model to study students’ understanding of fractions. Educational Studies in Mathematics, 64, 293–316.
Christou, C., Mousolides, N., Pittalis, M., Pitta-Pantazi, D., & Shiraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37, 149–158.
Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel.
Greer, B., & Verschaffel, L. (2007). Nurturing conceptual change in mathematics educaton. In S. Vosniadou, A. Baltas, & X. Vamvakoussi (Eds.), Reframing the conceptual change approach in learning and instruction (pp. 319–328). New York: Elsevier.
Harel., G., Koichu, B., & Manaster, A. (2006). Algebra teachers´ways of thinking characterizing the mental act of problem posing. In: J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (vol. 2, pp. 241–248). Prague, Czech Republic: Charles University.
Helus, Z. (2001). Čtyři teze k tématu změna školy [Four theses on the topic “Changing schools”]. Pedagogika, 51, 25–41.
Hošpesová, A., & Tichá, M. (2010). Reflexion der aufgabenbildung als weg zu erhöhung der lehrerprofesionalität [Reflection of problem posing as a way to professionalization of teachers]. In C. Böttinger (Ed.), Mathematik im Denken der Kinder. Anregung zur mathematikdidaktischen Reflexion [Mathematics in the minds of children. Suggestions for didactical reflection in mathematics] (pp. 122–126). Seelze: Klett/Kalmeyer.
Kieren, T. E. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101–144). Columbus: ERIC/SMEAC.
Koman, M., & Tichá, M. (1998). On travelling together and sharing expenses. Teaching mathematics and its applications, 17, 117–122.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: LEA.
Mewborn, D. (2001). Teachers content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Education Research Journal, 3, 28–36.
Pitkethly, A., & Hunting, R. (1996). A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30, 5–38.
Pittalis, M., Christou, C., Mousolides, N., & Pitta-Pantazi, D. (2004). A structural model for problem posing. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 49–56). Bergen, Norway: PME.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15, 4–14.
Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
Singer, F. M., Ellerton, N. F., Cai, J., & Silver, E. A. (2009). Problem posing in mathematics learning: Establishing a theoretical base for research. In: M. Tzekaki, M. Kaldrimidou, & H. Sakonidis, H. (Eds.) Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (vol. 1, pp. 299). Thessaloniki, Greece: PME.
Tichá, M. (2003). Following the path discovering fractions. In J. Novotná (Ed.), Proceedings of the International Symposium Elementary Math Teaching (pp. 17–26). Prague: Charles University, Faculty of Education.
Tichá, M. (2008). Wir lernen die missverständnisse und fehlvorstellungen der studenten zu beheben [We learn how to eliminate students´ misunderstandings and misconceptions]. In Beiträge zum Mathematikunterricht [Contributions to mathematics education] (pp. 761–764). Hildesheim: Franzbecker. Budapest.
Tichá, M. (2009). Problem posing in teacher training and as a research object in didactics: Two complementary perspectives. In: Quaderni di Ricerca in Didattica (Scienze Matematiche), Suplemento n. 2. Proceedings CIEAEM 61. Palermo: G.R.I.M. (pp. 445–449). Retrieved from: http://math.unipa.it/~grim/cieaem/quaderno19_suppl_2.htm.
Tichá, M., & Hošpesová, A. (2006). Qualified pedagogical reflection as a way to improve mathematics education. Journal for Mathematics Teachers Education, 9, 129–156. Special issue: Inter-relating theory and practice in mathematics teacher education.
Tichá, M., & Hošpesová, A. (2010). Problem posing and development of pedagogical content knowledge in pre-service teacher training. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, January 28th–February 1st March 2009, Lyon (France) (pp. 1941–1950). Lyon: Institut National de Recherche Pédagogique.
Toluk-Uςar, Z. (2008). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25, 166–175.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tichá, M., Hošpesová, A. Developing teachers’ subject didactic competence through problem posing. Educ Stud Math 83, 133–143 (2013). https://doi.org/10.1007/s10649-012-9455-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-012-9455-1